Long Island’s unemployment rate inched down to 3.9 percent in December from 4 percent a year earlier, state Labor Department data released yesterday show. It was the lowest rate for the month since 2007.

The number of unemployed residents fell by 2,200 to 56,800. Meanwhile, the number of people with jobs also fell by 11,900, to 1.4 million.

The drop in both the employment rolls and the jobless rate may indicate a growing number of retirees or discouraged workers, those residents who stopped looking for work because they didn’t believe they could find any. People not looking for jobs aren’t counted as unemployed.

“The aging population is causing the labor force to decline somewhat,” said James Brown, a labor-market analyst based in the department’s Brooklyn office.

And in a growing employment market, some weak sectors may produce discouraged workers, he said.

“Even in a strong market, some areas do better than others, and people don’t necessarily easily transfer from a declining sector to a growing one,” Brown said.

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The jobless rate probably won’t drop much more, and job gains may slow because the Island is at full employment, said John A. Rizzo, chief economist of the Long Island Association, the region’s largest business group. The classic economic definition of full employment is a jobless rate below 4 percent.

“We’re staying in a steady state of full employment,” he said. “Further job gains will be expected to be slower, and you would expect more wage increases.”

The latest report, based on a Census survey of residents regardless of where they work, comes a week after the department released data from Long Island businesses showing that the Island’s employment market grew at an annual rate of 17,300 jobs in December. It was the fastest pace in nine months.

Nassau and Suffolk’s jobless rates ticked down 0.1 percentage point each, to 3.6 percent and 4.1 percent, respectively.

Among the Island’s municipalities, Southampton Town had the highest jobless rate, at 5.5 percent. North Hempstead and Smithtown tied for the lowest, 3.4 percent.

The department uses year-over-year comparisons because local data aren’t adjusted to reflect seasonal swings in employment. The comparable unemployment rates for the state and the nation were both 4.5 percent.